Robust distortion risk measures
针对绝对连续扭曲函数的扭曲风险度量，推导其在已知均值和方差且分布位于Wasserstein距离球内的最大最小值，给出VaR和Range-VaR的准显式界，并应用于投资组合优化和模型风险评估。
Abstract The robustness of risk measures to changes in underlying loss distributions (distributional uncertainty) is of crucial importance in making well‐informed decisions. In this paper, we quantify, for the class of distortion risk measures with an absolutely continuous distortion function, its robustness to distributional uncertainty by deriving its largest (smallest) value when the underlying loss distribution has a known mean and variance and, furthermore, lies within a ball—specified through the Wasserstein distance—around a reference distribution. We employ the technique of isotonic projections to provide for these distortion risk measures a complete characterization of sharp bounds on their value, and we obtain quasi‐explicit bounds in the case of Value‐at‐Risk and Range‐Value‐at‐Risk. We extend our results to account for uncertainty in the first two moments and provide applications to portfolio optimization and to model risk assessment.